40 PROCEEDINGS OF THE AMERICAN ACADEMY 



Joule's result in 1850 was referred to water at about 14° C, and 

 in 1878 to water at 16°. 5 C. Taking intervals in the above table of 

 from 6° to 12°, so that the mean shall be nearly 14° and 16°.0, I 

 find the following for the ratios : — 



1.0044 1.0042 



1.0042 1.0042 



1.0049 1.0040 



1.0047 1.0030 



1.0047 1.0035 



1.0052 1.0035 



Mean, 1.0047 1.0037 



So that we have the following for Joule's old and new values : — 



or 1 in 700 and 1 in 390 respectively. 



But the correction found in this way is subject to local irregulari- 

 ties, and it is perhaps better in many respects to get the equation 

 giving the temperature of Joule's thermometer on the air thermom- 

 eter. Let T be the temperature by Joule's thermometer, and t that 

 by the air thermometer. Then I have found 



< = 0.002 + 1.00125 r— .00013 {lOO— T'j [l — .003(100+ r) } 



The fiictor 1.00125 enters in the formula, probably because the 

 thermometer which Joule used to get the value of the divisions of 

 his thermometer was not of the same kind of glass as his standard. 

 The relative error at any point due to using the mercurial rather 

 than the air thermometer will then be 



E= 1 — j'' = —.00125 + .00000039 { 23300 — 666 < + 3 ^^ j 



From this I have constructed the following table. 



